The magnetism of monolayer FeSe in multiple environments

FeSe is an Fe-based paramagnetic superconductor with the simplest structure. The competition between the Néel and stripe magnetic order is believed to be one of the reasons for the absence of magnetic orders in FeSe. FeSe is recognized as a prototypical platform for competing magnetic interactions, including Néel, stripe and staggered antiferromagnetic coupling. However, the correlations between these magnetic orders and how they change with varying environmental conditions require further study. Here, we calculated the magnetic order of monolayer FeSe in three different environments: pure one, with slight lattice distortion and on SrTiO₃ substrate, by the first principles calculations. We find that in the calculated dispersion relation E(q) between the spin spiral energy E and spin spiral vector q of the monolayer FeSe structure, the stripe magnetic order M (π/2, π/2) has the lowest energy, and there is a flat E(q) between the wave vector X (π/2, 0) and Néel magnetic order 2X (π, 0), which are the degenerate E(q) states. The ground state of M and the highest density of states around 2X may be the reason for the competition of two magnetic orders. The slight lattice distortion does not alter the magnetic properties of monolayer FeSe. When monolayer FeSe is attached to the SrTiO₃ substrate, the degenerate E(q) is still retained, meanwhile, the energy of 2X (π, 0) state is closer to M state, which may be one of the reasons for the increase of superconducting temperature in FeSe/SrTiO₃.